This year I plan to try to put together two ideas into one amazing or mess of a lesson.
Tomorrow this is the plan.
1. Introduce the Myth of trying to fold a piece of paper more than 7 times. We will discuss this problem and probably have a couple students try to do it. Hopefully we will get to the point that students realize that every time you fold the paper, the next fold is twice as hard.
2. We will introduce the Mythbusters clip about the paper folding myth. The paper size will be given to the students and they will calculate the area of the paper. The students will be asked to answer the following questions:
How many times will they be able to fold the paper?
What will the area of the paper be when they are done?
3. We will then watch the paper folding clip on Mythbusters.
4. We will discuss the results and the students' answers.
At this point I don't expect students to come up with any kind of equation, although some might. I just hope they get how fast exponential decay happens.
5. We will then turn the discussion to how the paper grows in height when it is folded. We will watch the first part of this TED ED video. It talks about how paper grows in height as it is repeatedly folded.
6. I will ask students to answer the following question:
How tall will the paper be after it is folded 30 times.
7. We will then watch the rest of the video. Again, I don't expect students to come up with an equation at this point. I just hope they realize the idea of exponential growth.
I am not sure this will be more effective than rice on a checkerboard, but I hope it will get the students thinking. I think the problems and videos relate nicely to each other and show both the idea of exponential decay and exponential growth.